The leaning tower of pisa is an architectural wonder

 

Question #6 (use the following to solve a, b, and c below)

 

The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the tower’s stability have done extensive studies on its increasing tilt. The following table shows how the lean has changed in excess of 2.9 meters by year since 1975.

 

 

 

A regression analysis was run on this data, and the results from Excel are shown below.

 

 

 

 

  1. What would Ho and Ha be to show whether the regression line is useful?

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. What is the result of the significance test tied to the regression line? Use α = 0.05. SOLVE AND INTERPRET CLEARLY AND THOROUGHLY.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. What is the equation of the regression line? (if it in fact exists)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7) From a, b, c and d below, circle the statement that is actually valid.

 

 

 

  1. A significance test is important because it proves without a shadow of a doubt that an outcome, ie result, is real and will never be wrong.

 

 

 

  1. Rejecting the null hypothesis means that the outcome of the significance test should be repeatable under similar circumstances, ie experimental conditions.

 

 

 

  1. If a p-value is very large, it means that the result of the significance test was highly likely, therefore under similar circumstances, a similar result can also be repeatedly achieved.

 

 

 

  1. The confidence level of a confidence interval indicates how often the random quantity known as the population mean will be located within a confidence interval.

 

 

 

 

 

 

 

 

 

Question #8(use the following to solve a, b, c, d, and e below)

 

An engineer working for a leading electronics firm claims to have invented a process for making longer-lasting TV picture tubes. Tests run on 24 picture tubes made with the new process show a mean life of 1,725 hours. Tests run over the last 3 years on a very large number of TV picture tubes made with the old process consistently show a mean life of 1,538 hours and a standard deviation of 85 hours.

 

If you would like to test whether the engineer’s work has produced a picture tube that definitely lasts longer, what would be…

 

  1. … the null hypothesis?

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. …the alternative hypothesis?

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. …the test statistic?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. …the critical value? (Use α = 0.05)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. …the result of the significance test? Note: BE THOROUGH. Do NOT just answer Reject or Fail to Reject.

 

 

 

 

Question #9

 

Professor Jane Newman teaches an introductory calculus course. She wanted to test the belief that suc cess in her course is affected by high school performance. She collected the randomly selected data listed below and ran an ANOVA test as shown below. The data in the “High School Record” table represents performance of the student in Jane’s calculus.

 

Anova: Single Factor

 

 

 

 

 

 

 

 

 

 

 

 

SUMMARY

 

 

 

 

 

 

Groups

Count

Sum

Average

Variance

 

 

Good

5

437

87.4

23.8

 

 

Fair

7

484

69.14285714

117.1428571

 

 

Poor

6

357

59.5

45.5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ANOVA

 

 

 

 

 

 

Source of Variation

SS

df

MS

F

P-value

F crit

Between Groups

2162.442857

2

1081.221429

15.81415676

0.000202214

3.682320344

Within Groups

1025.557143

15

68.37047619

 

 

 

 

 

 

 

 

 

 

Total

3188

17

 

 

 

 

 

High School Record

Good

Fair

Poor

90

80

60

86

70

60

88

61

55

93

52

62

80

73

50

 

65

70

 

83

 

 

 

 

 

 

a) If we set α at 0.05, what would we conclude about the ANOVA test? State the null hypothesis and result clearly. Give a reason for your result.

 

 

 
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